Here is an interesting look at the tetrations (infinitely repeating powers) of some fractions.
As a side note, we see that infinitely repeating powers of 1/4 could equal one product of repeating powers of 1/16
. Download 565_multi powers 2.mw
http://www.mapleprimes.com/files/565_multi%20powers%202.mw
This worksheet shows that the graph of repeated powers is a smooth curve in some of its domain then becomes "bent" for little reason. Perhaps someone can explain why it behaves so “unruly.”
